Talk:Alkmini

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Compilation strategy

Here are the notes I made while determining how to compile Alkmini to Kwert. Each Alkmini step is evaluated over five Kwert cycles, which I refer to as "phases". I define a list of variables used to track the numbers involved; a list of commands that appear at the beginning of the program in every phase; and, for each phase, three lists of commands describing parts of the program: the start, the cell, and the end. The start appears once after the shared beginning; the cell is repeated some number of times following the start, representing the symbols of the Alkmini program; and the end appears once following the cells. Commands that will be evaluated in the current phase are bolded.


variables:

  • nS: number of symbols in the program
  • nL: library size
  • nT: maximum number of symbols produced by any transition
  • nC: catalog size, determined by constructing the list of commands described below and inserting enough padding to make the size a near-square
  • rC: a near-square-root factor of nC
  • nD: intermediate catalog size, determined by constructing the list of commands described below and inserting enough padding to make the size a near-square
  • rD: a near-square-root factor of nD
  • Cb: size of a phase 2 cell = 2 + nL + 2 + nT + 2 + rP + nC
  • Cd: size of a phase 4 cell = 1 + rD + nT
  • Ce: core size of a phase 5 cell = 3 + rC
  • nB: size of skipped commands at the beginning = 5 + 4 + nC + 2 + rP + nD + nT * Ce - 2 + 1
  • nP: size of padding that goes in front of the catalog and intermediate catalog, based on a minimum value rounded up to a near-square
    • strictly speaking, the minimum would be based on the distances used by non-skipped phase 2 and 5 commands and the amount of commands they copy (in catalog-halt-library order for the former)
    • i believe though that the maximum of nD, Cb, and Cd would be a safe value (this does mean that Cb and nP have a cyclic dependency)
  • rP: a near-square-root factor of nP
  • i: 0-based index in a sequence of commands


shared beginning:

  • start skipper: automatically skipped
  • start skipper:
    • copy start skipper at dist 1
    • skip nB commands
  • phase 1 handler: skipped
  • phase 2 handler: skipped
  • phase 3 handler: skipped
  • phase 4 handler: skipped
  • phase 5 handler: skipped
  • beginning padding pre-generator: skipped
  • beginning catalog generator: skipped
  • intermediate padding pre-generator: skipped
  • intermediate catalog generator: skipped
  • nC skipped commands constituting the catalog:
    • nS intermediate symbol commands
    • empty intermediate symbol
    • some amount of padding no-ops
    • 2-skipper followed by 2 skipped no-ops
    • 3-skipper followed by 3 skipped no-ops
    • transition pre-skipper followed by 1 + nT skipped no-ops, if it's distinct from the 2-skipper and 3-skipper
    • transition skipper followed by nT skipped no-ops
  • no-op preserver: skipped
  • no-op: skipped
  • rP padding generators: skipped
  • nD skipped commands constituting the intermediate catalog:
    • symbol commands, padding pre-generators, catalog generators, and no-ops, laid out such that:
      • there are (potentially) multiple copies of each spaced at multiples of Ce as necessary for them to be copied by intermediate symbol commands at different offsets
      • every padding pre-generator has a catalog generator before it, to ensure that there's a minimal distinct sequence that can be used to identify a phase-1 symbol in the compiled program
      • padding no-ops are inserted as necessary
    • symbol skipper
    • Ce - 1 no-ops
  • nT * Ce - 2 no-ops: skipped
  • halt skipper: skipped


phase 1

start:

  • phase 1 handler:
    • copy phase 2 handler at dist nB - 1
    • copy no-op at dist 3
    • copy nL + 2 + nT - 1 no-ops at dist 1
  • beginning padding pre-generator: copy no-op preserver, no-op, and rP padding generators at dist nL + 2 + nT - 1 + 2 + nB - 5 - 4 - nC
  • rC beginning catalog generators: copy nC/rC commands at dist rP + 2 + nL + 2 + nT - 1 + 2 + nB - 5 - 4
  • some amount of no-ops

cell:

  • potentially, some amount of no-ops
  • symbol command:
    • copy halt signal, either at dist Cb or at dist from Cb - 2 to Cb - 1 - nL
    • copy no-op at dist 2
    • copy nL commands, each at dist from i + 1 to i + 2 + nC, composed of some mix of:
      • an intermediate symbol command
      • empty intermediate symbol
      • halt skipper followed by no-op
      • no-op
    • copy transition pre-skipper at dist nL + 2 + nT + 1 + 1 + nT + 1 (maybe + 2 in some cases if it turns out to be possible for nT to be 1 and thus for the transition pre-skipper to be the same as the 2-skipper?)
    • copy transition skipper at dist 1 + nL + 2 + nT + 1
    • copy nT commands, each at dist from 2 + nL + 2 + Cb - 1 - nL to 2 + nL + 2 + Cb - 2, and each being either:
      • an intermediate symbol command
      • empty intermediate symbol
  • padding pre-generator: copy no-op preserver, no-op, and rP padding generators at dist Cb
  • rC catalog generators: copy nC/rC commands at dist Cb

end:

  • potentially, some amount of no-ops (from a former preceding cell)
  • either:
    • halt skipper:
      • copy 3-skipper at dist nT + 1 + (1 + nT + 1 if transition pre-skipper is distinct from 3-skipper and 2-skipper) + 4
      • copy 2-skipper at dist 1 + nT + 1 + (1 + nT + 1 if transition pre-skipper is distinct from 3-skipper and 2-skipper) + 4 + 3
      • copy two more skipper pairs at dist 2
      • copy halt skipper or no-op at dist 6 + Cb
      • skip 1 command
    • no-op
  • halt: skipped or not depending on preceding command


phase 2

start:

  • phase 2 handler: copy phase 3 handler at dist nB - 2
  • nL + 2 + nT no-ops
  • no-op preserver: skip 1 command
  • no-op: skipped
  • rP padding generators
  • nC commands constituting a catalog

cell:

  • halt skipper or no-op
  • no-op: skipped or not depending on preceding command
  • nL commands, composed of some mix of:
    • an intermediate symbol command
    • empty intermediate symbol
    • halt skipper followed by a (skipped) no-op
    • no-op
  • transition pre-skipper: skip 1 + nT commands
  • transition skipper: skipped
  • nT skipped commands, each either:
    • an intermediate symbol command
    • empty intermediate symbol
  • no-op preserver
  • no-op: skipped
  • rP padding generators: copy nP/rP no-ops at dist 1
  • nC commands constituting a catalog

end:

  • 3-skipper: skip 3 commands
  • 2-skipper: skipped
  • 3-skipper: skipped
  • 2-skipper: skipped
  • 3-skipper: skip 3 commands
  • 2-skipper: skipped
  • halt skipper or no-op: skipped
  • halt: skipped


phase 3

start:

  • phase 3 handler:
    • copy phase 4 handler at dist nB - 3
    • copy intermediate padding pre-generator at dist 1 + nB - 5 - 2
    • copy intermediate catalog generator at dist 2 + nB - 5 - 3
    • copy rD - 1 intermediate catalog generators at dist 1
    • copy empty intermediate symbol from catalog at dist rD + 2 + nB - 5 - 4 - nS
    • copy nT - 1 empty intermediate symbols at dist 1
  • some amount of no-ops

cell:

  • some amount of no-ops
  • transition skipper:
    • copy intermediate padding pre-generator at dist Cd
    • copy rD intermediate catalog generators
      • could copy the generators all at once at dist Cd, or copy one at dist Cd + 1 - rD and the rest at dist 1
    • skip nT commands
  • nT skipped commands (same as before)
  • some amount of no-ops

end:

  • 2-skipper: skip 2 commands
  • 3-skipper: skipped
  • 2-skipper: skipped
  • 2-skipper: skip 2 commands
  • halt skipper or no-op: skipped
  • halt: skipped


phase 4

start:

  • phase 4 handler: copy phase 5 handler at dist nB - 4
  • intermediate padding pre-generator
  • rD intermediate catalog generators
  • nT empty intermediate symbols

cell:

  • intermediate padding pre-generator: copy no-op preserver, no-op, and rP padding generators at dist nT * Ce + nD + rP + 2
  • rD intermediate catalog generators: copy nD/rD commands at dist nT * Ce + nD + rP + 2
  • nT commands, each either:
    • an intermediate symbol command:
      • copy symbol skipper at dist Ce
      • copy corresponding symbol command at dist from 1 + Ce + 1 to 1 + nD
      • copy padding pre-generator at dist from 2 + Ce + 1 to 2 + nD - 1
      • copy catalog generator at dist from 3 + Ce + 1 to 3 + nD
      • copy rC - 1 catalog generators at dist 1
    • empty intermediate symbol:
      • copy symbol skipper at dist Ce
      • copy no-op at dist from 2 to 1 + nD
      • copy 1 + rC no-ops at dist 1

end:

  • 3-skipper: skip 3 commands
  • 2-skipper: skipped
  • halt skipper or no-op: skipped
  • halt: skipped


phase 5

start:

  • phase 5 handler:
    • copy phase 1 handler at dist nB
    • copy beginning padding pre-generator at dist 1 + nB - 5
    • copy beginning catalog generator at dist 2 + nB - 5 - 1
    • copy rC - 1 beginning catalog generators at dist 1
  • no-op preserver: skip 1 command
  • no-op: skipped
  • rP padding generators
  • nD commands constituting an intermediate catalog
  • nT instances of:
    • symbol skipper
    • 2 + rC no-ops: skipped

cell:

  • on every nTth cell, starting with the first:
    • no-op preserver: skip 1 command
    • no-op: skipped
    • rP padding generators: copy nP/rP no-ops at dist 1
    • nD commands constituting an intermediate catalog
  • symbol skipper: skip 2 + rC commands
  • either:
    • non-empty cell:
      • a symbol command: skipped
      • padding pre-generator: skipped
      • rC catalog generators: skipped
    • 2 + rC no-ops: skipped

end:

  • 2-skipper: skip 2 commands
  • halt skipper or no-op: skipped
  • halt: skipped

Arctenik (talk) 23:31, 5 March 2026 (UTC)

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